Question

В трапеции АВСД (ВС||АД), О - точка пересечения диагоналей, ВО=4 см, ОД=10 см, АС=21 см. Определите ОС. Варианты ответа: а) 6 см б) 8,2 смв) 15 см г) другой ответ

Answer 1

6 см = а.
4/10=х/21-х
10х=84-4х
14х=84
х=6. 

Answer 2

Solution for Finding OS in Trapezoid ABCD

To find the length of OS in trapezoid ABCD, where AB || CD, O is the point of intersection of the diagonals, VO = 4 cm, OD = 10 cm, and AC = 21 cm, we can use the following steps:

1. Use the Diagonals and Their Intersection Point: - The diagonals of a trapezoid bisect each other. This means that the point of intersection of the diagonals, O, divides each diagonal into two equal parts. Therefore, VO = OD.

2. Calculate the Length of OS: - Since VO = OD, we can find the length of OS by subtracting VO from the length of the entire diagonal OD.

3. Apply the Given Measurements: - Substitute the given values of VO and OD to calculate the length of OS.

Calculation

Given: - VO = 4 cm - OD = 10 cm

We can calculate the length of OS using the following formula: OS = OD - VO

Substitute the given values: OS = 10 cm - 4 cm OS = 6 cm

Therefore, the length of OS in trapezoid ABCD is 6 cm.

This calculation is based on the properties of trapezoids and the given measurements of the diagonals and their intersection point.

(#1)